Example 1:

This example is taken from AoPS Online and the result is that sum of first \(n\) odd numbers equals \(n^2\). \[ 1 + 3 + 5 + \ldots + (2n – 1) = n^2 \] The gganimate version of the proof (using the method in AoPS Online) is shown below (R code, html file)

Example 2:

This example is also taken from AoPS Online and the result is:

\[ 1^3 + 2^3 + \ldots + (n-1)^3 + n^3 = (1 + 2 + \ldots + n)^2 \] The gganimate version of the proof (using the method in AoPS Online) is shown below ( R code, html file):

Example 3

This example from AoPS Online illustrates the result

\[ \frac{1}{2^2} + \frac{1}{2^4} + \frac{1}{2^6} + \frac{1}{2^8} + \ldots = \frac{1}{3} \] The gganimate version of the proof (using the method in AoPS Online) is shown below ( R code, html file):

Example 4

According to Pythagoras theorem, \[ a^2 + b^2 = c^2 \] where \(a\), \(b\), \(c\) are sides of a right angled triangle (with \(c\) being the side opposite \(90^o\) angle)

There was an illustration of the proof of pythogoras theorem in a video from echalk.

The gganimate version of the proof is shown below ( R code, html file)

In summary, it was great to use gganimate for these animations since it does all the magic with making transitions work nicely.